A Variational Rayleigh–Ritz Method for Modeling $H$ -Plane Bend Rectangular Waveguides

This article introduces a novel variational formula for modeling waveguides with uniformly curved longitudinal axes. Using the Rayleigh–Ritz method, we analyze the electromagnetic fields in
$H$
-plane bend rectangular waveguides. In addition, we present a Galerkin method solution (GMS) for discretizing the associated vector Helmholtz equation within a local curved coordinate system. The proposed methodologies are validated through comparison with analytical results and a Galerkin-based solution from the literature across several representative scenarios. The rate of convergence, with respect to the number of expansion terms in the Rayleigh–Ritz method solution (RRMS), is observed to be faster than that in Galerkin-based solutions, while requiring comparable computational times. Furthermore, we explore the impact of both dielectric and conduction losses via the Rayleigh–Ritz method, aspects previously unattainable with analytical methods.